HiMoDe

This project is devoted to the low-frequency (LF) vibration analysis of dynamical structures having a high modal density in the LF band. The increasing complexity of dynamical structures in many industrial fields (automotive, aerospace…) induces an increase of the LF modal density and requires new predictive and efficient tools for the analysis of their complex dynamical behavior. The frequency spectrum of such structures is characterized by the presence of well separated global elastic modes which are coupled with a large number of local elastic modes in this LF band. Therefore, the classical modal analysis, which is known to be efficient for the case of well-separated resonances is no longer adapted in the investigated case. Furthermore, the global elastic modes cannot easily be separated from the local elastic modes. Indeed, due to the coupling between global elastic modes and local elastic modes, the deformations related to global elastic modes include some local contributions. In the same way, the deformations related to local elastic modes include global contributions. Thus, there are no efficient method which can be used to select the global elastic modes and the local elastic modes. In addition, although the Reduced-Order Model (ROM) must be constructed with respect to the global elastic modes, it must have the capability to predict correctly the dynamical behavior of the structure in this LF range. Since there are local elastic modes in the LF range, a part of the mechanical energy is transferred from the global elastic modes to the local elastic modes. These local modes store this energy and then induce an apparent damping at the resonances associated with the global elastic modes. There are three objectives in this project: (1) the first objective concerns the construction of a robust ROM by using a basis which is constituted of global modes and which is able to take into account the effects of the local displacements. To achieve this objective we propose to use a recent method which allows the extraction of a basis of global displacements and a basis of local displacements by solving two separated eigenvalue problems. The reduced modeling of the local contributions is the main issue for which this project aims to provide a solution. (2) The second objective is to construct ROMs in the context of slender complex dynamical structures which are characterized by a high modal density of local elastic modes in the LF band. Usually, the industry uses equivalent beam models (for which the validity is generally limited to the first resonances) to analyze this type of structure. We propose here to directly extract beam-like vectors in order to construct a ROM, which remains predictive in a large frequency domain. (3) The third objective concerns the dynamical analysis of non-linear structures (large deformations). The use of the modal analysis method to reduce the non-linear equations is prohibitive when the modal density is too high. We propose here to construct a ROM by using a global displacement basis and if needed by taking into account the effect of the local displacements. These three objectives would be achieved through: - Theoretical developments. - Experimental validations on a simple structure. - Several industrial applications. Concerning the final phase, the first industrial application concerns the construction of an efficient ROM of an automotive vehicle in collaboration with PSA Peugeot-Citroën. The second one concerns an application for the fuel assembly of a Pressurized Water Reactor in collaboration with EDF R&D. These researches aim at removing methodological locks and at providing non-intrusive methods directly usable by the involved engineers.